IN
DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM SWEDEN 2020,
FE-analysis of roller
creasing of corrugated board
ISAK HAMPEL KLANG
KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES
FE-analysis of roller creasing of corrugated board
Isak Hampel Klang September 1, 2020
Master Thesis SE202X - Degree Project in Solid Mechanics
Abstract
Creasing is often performed on paperboard to lower the bending stiffness in a region, making the paperboard easier to fold. Packsize AB uses rolls to crease corrugated paperboard. When using rolls for creasing double-walled corrugated paperboard in the machine direction, fracture occasionally occur on the top liner. This master thesis investigates the initiation of these surface cracks for a BC type corrugated paperboard. Experiments and FE-analysis are performed to study the magnitude of influence for various creasing roll geometries, under various hydraulic base pressures and changes in the material properties. The report includes a discussion of which material parameters that are the most sensitive with respect to surface crack initi- ation. Comparisons between FE-analysis and experiments are made to validate the FE-modeling. The experimental results show that the creasing roll geometries signif- icantly affects the percentage of failure. The best geometry lowered the percentage of failure from 36 % to 0 %. Furthermore, the most sensitive material parameters con- cerning the Tsai-Wu failure criterion used in the numerical simulations are Young’s modulus of the liners and the ultimate strength in the cross direction of the top liner.
A variation of 5 % of these material properties yields a change of the maximum Tsai- Wu strength index with 1.5 % and 5 %, respectively. However, further investigations with focus on validation and comparison of FE-analysis and experiments are needed to ensure a reliable model where various types and sizes of corrugated paperboard can be analyzed. This would need measured material properties as a part of the experimental study. Also, the performance of the yielded creasing lines from the experiments are not included in this thesis as well as the criticality of the top surface cracks.
Sammanfattning
Syftet med studien ¨ar att unders¨oka sprickbildning i den toopplinern av en dubbelv¨aggig wellpapp vid bigning med hjul i maskinriktningen. F¨or att studera inverkan av bign- ingshjul med olika geometrier vid olika hydrauliska bastryck samt f¨or¨andringar av materialparametrar har experiment och analyser med finita elementmetoden utf¨orts.
Inkluderat i arbetet ¨ar ¨aven att hitta de mest k¨ansliga materialparametrarna vad avser sprickbildning. J¨amf¨orelser mellan experiment och resultat fr˚an FEM har gjorts f¨or att validera modellen som anv¨ands f¨or FEM-ber¨akningarna. Resultaten visar att bigningshjulens geometrier b˚ade p˚averkar och kan minska risken f¨or sprickbildning i wellpappens toppliner. Den b¨asta geometrin p˚a bigningshjulet ger en minskning av det statistiska utfallet f¨or brott fr˚an 36 % till 0 %. Vidare framkommer att de mest k¨ansliga materialparamterarna med avseende p˚a det anv¨anda brottkriteriet ¨ar E-modulen och brottgr¨ansen i riktningen ortogonalt mot bigen. En variation med 5 % av dessa materialparametrar genererar en f¨orndring av det maximala Tsai-Wu styke indexet med 1.5 % respektive 5 %. Ytterligare unders¨okningar kr¨avs f¨or att fullst¨andigt f¨orst˚a beteendet vid bigning och inverkan av f¨or¨andringar av materialets egenskaper, bigningshjulens geometri samt olika bigningsdjup. Fortsatta experiment b¨or genomf¨oras f¨or att utvidga den bin¨ara unders¨okningaen av brotten till att ¨aven studera hur kritiska sprickorna ¨ar, hur l˚angt bigningen kan utf¨oras utan brott och bigad wellpapps b¨ojegenskaper.
Acknowledgements
This project was supervised by Michael Roos at Packsize AB, Enk¨oping, Sweden, and examined by S¨oren ¨Ostlund at Solid Mechanics Departments, KTH Royal Institute of Technology, Stockholm, Sweden.
I would like to express my gratitude to Artem Kulachenko, KTH, for his decisive input regarding contact settings for FE-analysis, Ronny, Packsize AB, for his sharing of knowledge about the creasing machine used in the experimental study, and S¨oren Ostlund for his input regarding previous research studies in this field of study, help¨ with limiting the thesis work and the support for writing the report.
Isak Hampel Klang Stockholm, Sweden August, 2020
Contents
1 Introduction 1
1.1 Problem definition . . . 1
1.2 Background . . . 1
1.2.1 Raw material . . . 2
1.2.2 Corrugated paperboard . . . 3
1.2.3 Manufacturing of corrugated paperboard . . . 4
1.2.4 Creasing . . . 5
2 Method and material 7 2.1 Experimental study . . . 7
2.2 Finite Element Analysis . . . 11
2.2.1 Material model . . . 11
2.2.2 FE-model of the corrugated paperboard . . . 13
2.2.3 Creasing rolls . . . 14
2.2.4 Element types . . . 16
2.2.5 Boundary conditions . . . 17
2.2.6 Displacement . . . 18
2.2.7 Delamination of fluting . . . 18
2.2.8 Failure criterion . . . 19
3 Results 21 3.1 Experiments . . . 21
3.2 FE-analysis . . . 21
3.2.1 Validation of model . . . 21
3.2.2 Creasing and stationary indenting . . . 25
4 Analysis 28
5 Discussion 29
6 Conclusions 30
References 31
Appendix 1 - Creasing roll geometries for experiments 34 Appendix 2 - Creasing roll geometries for FE-modeling 40
1. Introduction
Corrugated paperboard is a frequently used material in the packaging and shipping industry. The lightweight structure, low environmental effects, and high specific strength when stacking boxes are characteristics of corrugated paperboard. In boxes and containers, corrugated board is folded to get the desired geometries. To make paperboard easier to fold, creasing, also known as scoring, is performed to make pre-folding lines that locally lowers the bending stiffness. Creasing makes it easier to obtain a straight edge in the final box or container. When large amounts of boxes are manufactured, the production time per box is an important parameter that com- panies want to minimize. One method used by Packsize AB is a multi-axis toolhead cutting and creasing machine that can produce various box geometries. Here, we will call this roll creasing. The creasing itself is performed by compressing the cor- rugated paperboard between two closely mounted rings and a rubber roll, moving the corrugated paperboard in the machine direction. Twelve tool heads acting in the machine direction (MD) and one acting in the cross direction (CD) enable effi- cient processing and ability to change the geometry of the manufactured box without stopping for changing geometry tools. The creasing compresses the flutings of the corrugated paperboard, deforming them plastically, and sometimes fracture of the fluting material occurs. The method for creasing used by Packsize AB, also, occa- sionally, result in cracks on the top surface of the corrugated paperboard. Here, this will be investigated combining experiments and non-linear 3D finite element analysis.
The aim is to lower the risk of surface cracks when creasing double-walled corrugated paperboard using rolls.
1.1 Problem definition
This thesis investigates crack initiation on the top surface of a double-walled cor- rugated paperboard when creasing using rolls. Experiments and FE-analysis are performed where the aim is to find and determine the critical parameters and their relative magnitude concerning crack initiation. In addition, various geometries of the creasing rolls will be investigated. In this thesis, the analysis will be limited to a BC-type corrugated paperboard, creasing in the machine direction (MD) and the failures in the experimental study will solely be reported as fracture or no fracture.
1.2 Background
The diversity of paper gives a wide range of applications, such as printing paper, carton containers, corrugated paper boxes, etc. Boxes for transport packaging are commonly made of corrugated paperboard being a sandwich type of structure consist- ing of a combination of different packaging boards. The paper industry is expanding, due to factors such as low production costs, a wide range of applications, the ability to recycle, and the low environmental impact [1]. Paper is a stochastic material as described by Uesaka [2]. He investigate the statistical failure of paperboards, fol- lowing the process from production to finished product. He concludes that there are huge challenges in sorting out the dependent and independent factors. However, these problems have slowly been cleared out and some preliminary understandings are collected. Thus, the area of research needs new approaches to fully understand
the influence of all dependent variables. His research needs a full manufacturing and treatment investigation to statistically evaluate the material, something that this thesis will lack, which motivates a non-full evaluation. Kulachenko et al. [3] create a stochastic constitutive model for predicting the random mechanical response of isotropic material. His method is not yet applicable to larger non-linear mechani- cal problems such as this thesis. The stochastic behavior is one of the challenging characteristics of paper materials, especially including the macroscopic orthotropic behavior. Since both Kulachenko’s and Uesaka’s statistical methods are very exten- sive, no full statistical evaluation is performed.
The most common research performed on corrugated paperboards are related to characterization of the mechanical behavior and determination of material parame- ters, often investigating bending stiffness and edge loading to improve modeling of stacking of boxes. In the work of Allansson and Sv¨ard [4], and Nordstrand [5], the cor- rugated paperboard is successfully represented as a homogeneous sandwich material using approximated material properties for the core, representing the fluting. This is a sufficient method for investigating global behaviour of the paperboard. However, local behaviours such as fracture are hard to capture, especially for a double-walled corrugated paperboard with different wave-lengths in each core. Therefore, a 3D full- scale FE-model is chosen, also used and investigated by Allansson and Sv¨ard. A 3D full-scale FE-model give lots of contact regions which gives a highly non-linear model.
They also use the Tsai-Wu failure criterion [6] to predict failure in the material for a full FE-model. This is the most commonly used failure criterion for orthotropic ma- terials such as paper, with various approximation opportunities dependent on what material information that can be yielded with experiments. For thin structures such as paper, the shear modules can be hard to be determined experimentally and is often approximated as done by Nyman and Gustafsson [7]. Thakkar [8] and Gooren [9] investigate the creasing abilities of paperboards with combining experiments and 2D FE-analysis. Their research together with Allansson and Sv¨ard’s paper give un- derstanding of meshing, contacts and variation of creasing positions with respect to the flutings. However, double-walled corrugated paperboard is a considerably less investigated topic, especially the creasing performance of such paperboards.
1.2.1 Raw material
Paper is manufactured out of mainly fiber materials from wood. These are mechani- cal and chemical pulps, both made from fresh fibers. Recycled fibers are either from previously mechanical or chemical pulps. Each fiber material has several precise treatments that give the wanted chemical and mechanical properties [1]. Minerals are used for coating pigments that are used to improve the surface quality in terms of brightness, gloss, and smoothness. Minerals are also used as fillers enabling a paper variety of morphology, refractive index, chemistry, brightness, size of particles, hardness, and solubility [10].
1.2.2 Corrugated paperboard
Corrugated paperboard consists of several combined packaging boards. The flat parts are called liners and the wave-shaped cores are called fluting or medium. These are glued together giving the strong lightweight structure. Corrugated paperboard can consist of one or several flutings and liners to accommodate different applications and performances. The most common types are shown in Figure 1.1. This thesis will be focusing solely on double-walled corrugated paperboard.
Figure 1.1: Different kinds of corrugated paperboards, [11].
The coordinate system used for corrugated paperboard has normally the x-direction parallel to the direction of the wave-shaped flutings, which coincide with the machine direction (MD) of the packaging boards. The y-direction, also cross direction (CD), is orthogonal to the MD. The z-direction is normal to the surface, see Figure 1.1.
The characteristic dimensions of the wave-shaped flutings are shown in Figure 1.2.
Figure 1.2: Characteristic measurements of corrugated paperboard [4].
Here, λ is the wavelength of the fluting, h is the height of the fluting and tliner and tf lute are the thicknesses of fluting and liner, respectively. The local coordinate systems are also shown in the illustration, where the 1-, 2- and 3-direction for the liners coincide with the global system.
For the wave-shaped fluting, the local coordinate system has the 3-direction normal to the surface of the material, the 2-direction parallel to the global y-direction and the 1-direction is oriented in the local machine direction of the fluting.
There are standardized geometrical combinations of the fluting. The industrial stan- dards are listed in Table 1.
Table 1: Standard geometries of fluting height and wavelength for corrugated paperboard - ISO 4046 [12]. Slight deviations from stan- dards are common to accommodate certain performance [13].
Type Fluting height h [mm] Wavelength λ [mm]
A 4.8 9.1
B 2.4 6.7
C 3.6 7.7
E 1.2 3.4
F,G,N 0.5-0.8 1.8-2.5
For double-walled corrugated paperboards, the names, e.g. BC denotes that the upper fluting consists of type B and the lower fluting is of type C. The thicknesses of each paper board are not standardized. They can vary to accommodate certain usage.
1.2.3 Manufacturing of corrugated paperboard
A schematic illustration of the production of corrugated board can be seen in Figure 1.3. Each paperboard is stored as large rolls to accommodate long continuous man- ufacturing. These paperboards pass through a pre-heater (1), to improve the gluing and corrugating process. The pre-heater has a small adjustable roll that controls the time that the paperboards are in contact with the heater roll. The longer the paper- board is in contact with the pre-header, the higher temperature it will get. After the heating process, the flutings paperboard passes through the corrugator (2). The cor- rugator consists of two gear-shaped cylinders, where the paperboard is compressed between the cylinders that form it to the desired wave-shape fluting. The fluting is then in contact with a gluing machine (3), where glue is applied to the tips of the fluting. The gluing machine also has a metering roll that controls the amount of glue that is transferred to the fluting tips. Liner and fluting are glued together between a pressure roll (4) and the corrugator. This is done under controlled pressure to ensure a strong bond. These procedures (1-4) give a single-faced corrugated paper- board, consisting of a fluting and a liner. Depending on what type of corrugated paperboard that is produced, these procedures are performed once or several times to end up with a final combination of flutings and liners. When all paperboards are glued together, they pass through a drying panel (5) which dries the structure under pressure. When the paperboard is dried, it will be stored as stocks of cut (6) paper sheets or as z-folds [11].
Figure 1.3: Manufacturing machine for corrugated paperboard [11].
1.2.4 Creasing
Creasing is normally a deformation controlled procedure for paper structures that create a pre-fold on a paperboard that is meant to be folded. One widely used method for creasing is the die-creasing method. It uses a ruler and a die, where the ruler is indented into the paperboard, plastically deforming it. The female dies have often cavities that enable deformation of the entire paperboard as illustrated in Figure 1.4a [11]. Same indentation can also be performed continuously with a rotating cylinder.
This method is called rotary die-creasing, see Figure 1.4b [11]. These methods can often give lots of material waste as Figure 1.4b shows, which can be costly for the manufacturer. The setup is also for a specific box geometry and needs to be changed to produce another geometrical form. Another method, used by Packsize AB, has a multi-toolhead operation system. Here, the upper rotary die-creaser is replaced with twelve toolheads creasing in the MD, and one toolhead creasing in the CD. The toolheads are creasing by indenting creasing rolls instead of rulers. This setup gives the possibility to change the position of the creasing, enabling various box geometries to be manufactured one after another without interruptions, see Figure 1.4c. This method displaces the creasing rings using various pressure loadings.
(a) Die-creasing [11]. (b) Rotary die-creasing [11].
(c) Roller creasing.
Figure 1.4: Creasing methods.
For a corrugated paperboard, a creased paperboard typically looks like shown in Figure 1.5.
Figure 1.5: Cross sectional view of a corrugated paperboard that has been creased in MD.
The fluting of a corrugated paperboard is compressed and plastically deformed at the contact with the rule indent, making the structure locally weaker in bending.
This makes it easier to fold and reduce the risk of getting an oblique edge.
2. Method and material
The investigation of surface crack initiation is performed on a BC-type of a double- walled corrugated paperboard. The creasing experiments are performed with rolls at Packsize AB and the non-linear 3D FE-analysis investigating the influence of depen- dent variables. The experimental study is performed to investigate the occurrence of the fracture using different creasing roll geometries under various pressure loadings.
Since the FE-model does not consider stochastic material behavior, it is hard to com- pare the statistical outcome from the experiments with results from the FE-analysis.
Therefore, the experimental outcome will solely be evaluated binary, i.e. cracking or no cracking. It is the easiest and most suitable way to yield the statistical outcome from the experiments, even though it does not take the width, length of the formed cracks into consideration or how much the crack affects the performance of the edge.
2.1 Experimental study
Packsize AB has developed a multi-axis tool head operating creasing machine. It has ten toolheads creasing in MD, two side cutters in MD, and one toolhead acting in CD.
These can be moved orthogonally to the creasing direction and are pushed into the paperboard by a hydraulic base pressure that can be varied between 2 bar and 5 bar.
This allows changing the positions of cutting and creasing during manufacturing, also enabling different sizes and geometries of blanks to be manufactured one after another without stopping the production to change geometrical tools. The toolheads consist of a creasing tool, a cutting knife, and a tool that positions the creasing rolls and knives, also pushing the creasing rolls or knives into the paperboard. Instead of having a die indenting the surface of the corrugated paperboard, two closely mounted rolls of aluminum are pressed down into the corrugated paperboard. Underneath the creasing rolls, a rubber roll is supporting and moving the corrugated paperboard.
The creasing in MD is performed by moving the corrugated paperboard between the rubber roll and the creasing rolls that are pressed down into the upper surface of the paperboard. The rubber roll has no cavities as for die-creasing because of the possibility to change the positioning of the toolheads. Figure 2.1 shows the setup of the toolheads and the rubber rolls.
(a) Creasing toolhead in CD(1), a rubber roll(2), and a creasing toolhead in MD(3), with mounted creasing rolls.
(b) Setup for all the toolheads acting in MD, rubber rolls, and metal supporting rail.
Figure 2.1: Setup of present creasing machine.
In Figure 2.2 is a schematic illustration of the toolhead shown, where a creasing roll is illustrated in orange color, a cutting knife in blue, a rubber roll in green and the paperboard in brown.
Figure 2.2: Creasing setup, where δz is the indentation depth of the creasing roll into the corrugated paperboard.
A hydraulic base pressure displaces the creasing rolls into the surface of the corru- gated paperboard. The pressure is converted to force via two hydraulic cylinders that push the creasing rolls into the board. This base pressure can be expressed as a force acting on the pair of creasing rolls by
F = p(A1+ A2) (2.1)
where p is the hydraulic base pressure and A1 and A2 are the cross-sectional areas of the hydraulic cylinders. Here, the cross-sectional areas were 490 mm2 and 154 mm2, respectively. The base pressure can be varied between 2 bar and 5 bar. A schematic illustration of the hydraulic base pressure system can be seen in Figure 2.3.
Figure 2.3: Hydraulic pressure system.
The creasing experiments are performed with the base pressure from 2 bar to 5 bar.
To investigated the hypothesis that stationary indentation without rolling can be used in FE simulations. Experiments are also performed where the creasing rolls are stationary indented into the surface of the corrugated paperboard without moving the board. For the creasing experiments, the displacement, δz, of the creasing rolls into the paperboard are measured. Also, a binary investigation of the top surface of the paperboard is performed, where cracks along the creasing line are examined.
A typical fracture of the top liner of a corrugated paperboard can be seen in Figure 2.4, where the crack propagates in the MD.
Figure 2.4: Fracture of the top liner of corrugated paperboard using roll creasing.
The creasing rolls follow the geometries described in Appendix 1 and the cross-section of the original ring pair can be seen in Figure 2.5, where the gap between the rolls is 0.8 mm to enable the operation of the cutting knife.
Figure 2.5: Cross-section of original creasing roll. The gap between the two parts is 0.8 mm which enables the operation of the cutting knife.
The positions of the toolheads acting in the MD are investigated to ensure that the creasing lines do not affect each other being too closely positioned. In Figure 2.6, the positioning can bee seen.
Figure 2.6: Creasing roll positioning.
Here, the active creasing rolls are positioned with the same distancing, L, to each other, with the width of the paperboard, W , being 2000 mm. The distance L is varied for values of 5, 15 and 30 mm, respectively. A manufactured blank specimens from the experiments can be seen in Figure 2.7, where the distance from the end of the creasing lines to the edge of the paperboard ,D, is 50 mm and the length of the creasing lines, a, is 500 mm.
Figure 2.7: Blank, where D is the distance between the end of the creasing line and the outer edge of the corrugated paperboard and a is the length of the creasing line.
The experiments are performed with a commercially accessible BC corrugated paper- board from one of the leading contractors. This gives no possibility to validate the FE-analysis with the experimental results. However, comparisons with this general material is conducted.
2.2 Finite Element Analysis
2.2.1 Material model
Paper is an anisotropic material, often approximated as orthotropic, which means that it has different material properties in different directions. This is due to the orientation of the fibers, giving a typical local 1-, 2- and 3-orientation. This gives the stress-strain relation σ = Cε as
σ1
σ2
σ3
τ12
τ13
τ23
= A
E1(1 − ν23ν32) E1(ν21+ ν31ν23) E1(ν31+ ν21ν32) 0 0 0 E2(ν12+ ν32ν13) E2(1 − ν13ν31) E2(ν32+ ν12ν31) 0 0 0 E3(ν13+ ν12ν23) E3(ν23+ ν13ν21) E3(1 − ν21ν12) 0 0 0
0 0 0 G12
A 0 0
0 0 0 0 G13
A 0
0 0 0 0 0 G23
A
ε1
ε2
ε3
γ12
γ13
γ23
(2.2)
where A = 1/(1 − ν12ν21− ν13ν31− ν23ν32− ν12ν31ν23− ν21ν13ν32) and C is the stiffness tensor. Here, σ is the stress vector, Ei is the Young’s modulus in i-direction, νij is the Poisson’s ratio in in ij-direction, Gij is the shear modulus in in ij-direction and ε is the strain vector.
The material parameters, assigned to each part of the model, can be found in Table 2. These material properties do not correlate to the specific material properties of the paperboards used for the experiments. The material properties used for the FE-analysis are from an experimental study by Haj-Ali, et al. [14]. The elastic- plastic material model with orthotropic linear elasticity also has a bilinear isotropic hardening applied to the model, which means that the same plastic behavior was applied in all directions. This could over- or underestimate the stiffness of the model due to the inaccuracy of applying isotropic hardening for an orthotropic material.
The yield stress and the tangent modulus are chosen for tension in the y-direction [14]. This to accommodate an as good approximation of the failure initiation as possible since it was known that the direction of crack propagation is MD.
Table 2: Material properties for flutings, liners [14] and creasing rolls.
Assigned to Variable Value Description
Fluting
E1 4470 MPa Young’s Modulus E2 1610 MPa Young’s Modulus E3 17.9 MPa Young’s Modulus ν12 0.18 Poisson’s Ratio ν23 0.01 Poisson’s Ratio ν13 0.01 Poisson’s Ratio G12 1040 MPa Shear Modulus G23 226 MPa Shear Modulus G13 198 MPa Shear Modulus
σy 8.06 MPa Yield Stress Et 145 MPa Tangent Modulus
Liner
E1 4780 MPa Young’s Modulus E2 2090 MPa Young’s Modulus E3 19.1 MPa Young’s Modulus ν12 0.18 Poisson’s Ratio ν23 0.01 Poisson’s Ratio ν13 0.01 Poisson’s Ratio G12 1220 MPa Shear Modulus G23 166 MPa Shear Modulus G13 137 MPa Shear Modulus
σy 18.4 MPa Yield Stress Et 356 MPa Tangent Modulus Creasing roll E 200 GPa Young’s Modulus
ν 0.3 Poisson’s Ratio
The material properties of the creasing rolls are not dependent factors due to the large difference in stiffness compared to the paperboards. The influence of the pa-
2.2.2 FE-model of the corrugated paperboard
As explained in section 1.2.2, the corrugated paperboard is built up by liners and flutings. The BC type is built up by 3 liners and 2 fluting layers. In the FE-analysis, an approximation of the fluting was done as suggested by Allansson and Sv¨ard [4].
Instead of a wave-shaped fluting, the waves are approximated with 6 straight lines as shown in Figure 2.8. The liners and flutings are separate bodies, modeled as shells with assigned thicknesses.
Figure 2.8: Approximation of BC type of corrugated paperboard in the FE-model. The yellow lines are the liners, the green lines are the wave-shaped flutings and the black lines represents the approx- imation of the BC corrugated paperboard.
Figure 2.9 shows the definitions of the geometric parameters, where λi are the wave- lengths, hi are the heights of the flutings, tij are the thicknesses, Lij are the lengths of the different parts of the fluting and ϕij are the angles between the fluting segments and the liners.
Figure 2.9: Definition of the geometric parameters of the BC type of corrugated paperboard.
The size of the corrugated paperboard was parameterized to ensure that the model was sufficiently detailed to give robust analysis results. In Table 3, the geometric parameters of the model of the BC type corrugated paperboard BC are stated.
Table 3: Geometric parameters.
Model Variable Value Description
B-fluting
λB 6.7 mm Wavelength
hB 2.4 mm Height
tB 0.12 mm Thickness
LB1 1.35 mm Length of line segment LB2 1.50 mm Length of line segment LB3 1.35 mm Length of line segment ϕB1 27.5◦ Angle of LB1 ϕB2 50.3◦ Angle of LB2 ϕB3 27.5◦ Angle of LB3
C-fluting
λC 7.7 mm Wavelength
hC 3.6 mm Height
tC 0.12 mm Thickness
LC1 1.35 mm Length of line segments LC2 2.77 mm Length of line segments LC3 1.35 mm Length of line segments ϕC1 27.5◦ Angle of LC1 ϕC2 58.2◦ Angle of LC2 ϕC3 27.5◦ Angle of LC3 Liners tliner 0.12 mm Thickness
The relative position of the liners and the flutings can be modeled with or without an offset, as illustrated in Figure 2.10. Here, the corrugated paperboard was modeled without offset to yield less complicated non-linear contacts [4].
(a) No offset modelling of corrugated paper- board.
(b) Offset modelling of corrugated paper- board.
Figure 2.10: Offset options.
2.2.3 Creasing rolls
The modeling of the creasing rolls only needs to include the parts that will be in
In addition, a part is added to the rolls to enable application of symmetry boundary conditions. In Figure 2.11a, the parts that are included in the model can be seen and in Figure 2.11b the additional part is highlighted in orange. The geometries of the creasing rolls used in the FE-model can be found in Appendix 2.
(a) Parts included in FE-modelling. (b) Additional part for symmetry condition.
Figure 2.11: Modeling of the creasing roll for FE-analysis.
The rolls are positioned in contact with the top liner of the corrugated paperboard as shown in Figure 2.12.
Figure 2.12: Positioning of the creasing roll.
Since the wave-length for the the two flutings vary is the position of the creasing roll in the x-direction a dependent variable, meaning that different positions give various mechanical problems. The most critical position is ought to be found with respect to the failure criterion. This position is found by parameterizing the location of the creasing roll. This is further explained in section 2.2.6.
2.2.4 Element types
The solving time for FE-analysis is highly dependent on the number of elements and degrees of freedom in the model. For the paperboards, shell elements are used since they are suitable for thin structures such as paper. There are different types of shell elements, which are built up by various amount of nodes and degrees of freedom.
Here, the element type used for the corrugated paperboard is 4-noded quadrilateral shell elements with 6 degrees of freedom; i.e. translations in the x-, y-, z-directions, and rotations around the x-, y-, z-axes. The creasing rolls are modeled with 8-noded quadrilateral solid elements with 3 degrees of freedom per node; i.e. translations in x-, y-, z-directions [15].
It is desirable that the number of elements is as low as possible, without losing accu- racy in the results. The choice of mesh is often motivated by results from performed mesh convergence studies, where the size of the mesh elements are parameterized and the influence of the changes are investigated. As for the element types, the choice of mesh method can affect the results. The nodes at the connections between the paperboard parts are positioned so that they coincide with each other. This can be seen in Figure 2.13 for the upper liner and the B-fluting.
Figure 2.13: Position of nodes at the connections between flutings and liners.
The investigation of the mesh for the paperboard was performed by changing the number of elements along various edges of the paperboard. This method was chosen to ensure that the nodes of the liners always coincide with the fluting tips. The mesh of the creasing rolls was parameterized by the element size. The importance of the mesh of the creasing roll, apart from contributing to a robust model, was to ensure that the specific geometries of the creasing rolls were captured. All the mesh convergence studies was performed using the failure criterion presented in section 2.2.8, for the top liner. Here, the wanted result was a robust model with results that had converged so that small changes in mesh size, did not, to any greater extent, affect the results.
2.2.5 Boundary conditions
The contact between the liners and flutings are modeled as a bonded line contact, meaning that it can not lose contact or slip. In Figure 2.14, two contact lines are illustrated in red. The same contact type was applied between all liners and fluting tips.
Figure 2.14: Bonded contact lines highlighted in red.
When the corrugated paperboards are creased, the fluting is compressed between the liners. To model this effect, a frictionless contact was applied between each surface of the liner and fluting. When contact is detected between liner and fluting, no penetration is allowed. A frictionless contact was also applied between the outer surface of the creasing roll and the top liner, which is the crucial contact between the roll and corrugated paperboard in the present model. In the initial time-step, the creasing roll is in contact with the top liner to reduce initial contact calculations.
A symmetry condition was also applied to the model, giving lower computational costs and fewer elements in the model. The symmetry plane can be seen in Figure 2.15.
Figure 2.15: Symmetry plane, symmetry shown in red.
The lower liner was not allowed to move in the z-direction. This is a mere repre- sentation of the rubber roll supporting the corrugated paperboard from underneath in the experiments. However, this is not a perfect representation of the rubber roll.
Since the investigation of this creasing method is focusing on the effects of the creas- ing rolls, the surface underneath the corrugated paperboard was approximated to a plane rigid surface. Also, to ensure no rigid body motion, a fixed point was chosen at the edge of the model in the symmetry plane. These boundary conditions can be seen in Figure 2.16.
Figure 2.16: Global boundary conditions.
2.2.6 Displacement
The movements of the creasing rolls are done by displacing the outer surface of the rolls that are going to be in contact with the corrugated paperboard. Since all these surfaces are simultaneously displaced, this corresponds to a rigid representation of the creasing rolls, making the material independent of the modelling. The modeling of the creasing is done by first, displacing the creasing rolls into the corrugated pa- perboard to the depth, δz. Thereafter, the creasing rolls are displaced in the MD.
The creasing depth, δz, is the value that has been measured from the experiments.
The creasing depth is defined in Figure 2.2. All mesh and size convergence investiga- tions were performed with stationary indention. This means that the displacement was only performed in the z-direction. Here, a value of δz = 3 mm was used.
2.2.7 Delamination of fluting
Delamination of folded paperboards is a known problem. Nyg˚ards [16] analyses the phenomenon of delamination of folded carton board boxes. He shows that delam- ination can occur during creasing as illustrated in Figure 2.17. The corrugator in the manufacturing process of corrugated paperboard is deforming the paperboard in a similar way as for die-creasing with cavity (Figure 2.17a). This motivates that delamination, can occur at the corrugator in the manufacturing process.
(a) Parts included in FE-modelling. (b) Addition part for symmetry condition.
Figure 2.17: Delamination of paperboard [16]
Delamination lowers the shear moduli in local 1-2-plane of the fluting. To investigate the effects of this phenomenon on properties of the fluting, the shear modulus of the middle part were parameterized as highlighted in Figure 2.18.
Figure 2.18: Highlighted in orange are the parts of the fluting where delamination is assumed.
2.2.8 Failure criterion
A failure criterion was used to predict potential fracture locations in the structure.
The most commonly used in analysis of paper structures is the Tsai-Wu failure crite- rion [6]. It is determined by directional stresses and material strengths in local x-, y- and z-directions, making it suitable for orthotropic materials with large deformations such as paper since the local coordinate system is considered. The criterion gives a strength index that indicates if an element or material will fail or not. The Tsai-Wu strength index is calculated from
fT W =
σx σy σz τxy τxz τyz
T
F1 F2 F3 0 0 0
+
σx σy σz τxy τxz τyz
T
F11 F12 F13 0 0 0 F21 F22 F23 0 0 0 F31 F32 F33 0 0 0
0 0 0 F44 0 0
0 0 0 0 F55 0
0 0 0 0 0 F66
σx σy σz τxy τxz τyz
(2.3)
Symmetry, Fij = Fji, and plane stress simplifies Eq. (2.3) to
fT W = F1σx+ F2σy+ F11σx2+ F22σ2y+ F44τxy2 + 2F12σxσy (2.4) where the constants expressed in terms of measured properties are given in Table 4.
The Tsai-Wu strength index indicates failure when fT W > 1.
Table 4: Expressions for the Tsai-Wu constants [17], where the expressions for F12 and τxy follows from Nyman et al. [7].
Parameter Expression F1
1 σxtf − 1
σxcf
F2 1
σytf − 1 σycf
F11 1
σxtfσxcf
F22
1 σytfσycf
F44 1
τxyf
2
F12 −0.36√ F11F22 τxyf 0.78
q σxcf σfyc
Paper is a stochastic material with local fluctuations in the material properties. How- ever, no stochastic material behavior was implemented in the FE-analysis. Therefore, a parameterization of the ultimate strengths was performed to get information on the sensitivity of the parameters and to identify which one that are most critical.
The ultimate strengths assumed for the top liner are found in Table 5.
Table 5: Ultimate strength parameters [14]. Sub-indices t and c refers to tension and compression, respectively.
Ultimate strength parameters σxtf σfxc σfyt σycf Values Liner [MPa] 59.4 23.8 28.0 16.3
3. Results
3.1 Experiments
The outcome of the experiments with different creasing roll geometries at different base pressure are presented in Table 6.
Table 6: Experimental results - Number of fractured specimens for different creasing roll geometries at different base pressure.
Creasing roll number 2 Bar 3 Bar 4 Bar 5 Bar
0
Number of tests 45 50 45 50
Number of fractured specimens 2 6 16 23
Percentage of failure 4 12 36 46
1
Number of tests 6 8 6 8
Number of fracture specimens 2 7 6 8
Percentage of failure 33 88 100 100
2
Number of tests 6 8 6 8
Number of fractured specimens 1 4 5 6
Percentage of failure 17 50 83 75
3
Number of tests 12 12 12 12
Number of fractured specimens 1 4 5 6
Percentage of failure 0 17 58 75
4
Number of tests 6 6 6 6
Number of fractured specimens 1 0 0 0
Percentage of failure 17 0 0 0
5
Number of tests 6 6 6 6
Number of fractured specimens 0 1 5 6
Percentage of failure 0 17 83 100
The measured creasing depth, δz, for roll creasing and stationary indentation at a pressure of 4 bar are presented in Table 7.
Table 7: Depths for creasing and stationary indentation with a pres- sure of 4 bar.
Creasing roll geometry 0 1 2 3 4 5
Mean δz roll creasing [mm] 4.72 4.73 4, 75 4.74 4.75 4.73 Mean δz stationary indenting [mm] 4.75 4.75 4, 71 4.67 4.80 4.78
3.2 FE-analysis
3.2.1 Validation of model
This section will solely show results when using the original creasing roll geometry.
The influence of the size of the model was investigated with respect to the Tsai-Wu strength index. Figure 3.1 shows the deformation field in the z-direction.
Figure 3.1: Deformation field, uz, of top liner of the BC corrugated paperboard paperboard for l = 130 mm, w = 100 mm, and δz = 4.75 mm.
The region in red has a deformation smaller than 0.1 mm. This gives an indication of the required size of the corrugated paperboard model. Different sizes were inves- tigated and the values of the Tsai-Wu index were compared. The results from this investigation can be seen in Figure 3.2 where the maximum Tsai-Wu strength index is shown for different values of both model width, w, and model length, l.
Figure 3.2: Maximum Tsai-Wu strength index for different length,
The results from the mesh convergence studies for liners, flutings and roll are shown in Figure 3.3-3.5.
Figure 3.3: Maximum Tsai-Wu strength index for different mesh sizes of the flutings. w = 100 mm and l = 80 mm. δz = 3 mm.
Figure 3.4: Maximum Tsai-Wu strength index for different mesh size of the liner and fluting in y-direction. w = 100 mm and l = 80 mm. δz = 3 mm.
Figure 3.5: Maximum Tsai-Wu strength index for different mesh size of the creasing roll. w = 100 mm and l = 80 mm. δz = 3 mm.
The chosen final mesh is explained by Figure 3.6 and Table 8.
Figure 3.6: Representative description of the final mesh, see Table 8.
Table 8: Mesh size for lines of the corrugated paperboard.
Description
Edges of the liners Edges of the Edges of the Creasing and the flutings liners parallel to flutings in roll parallel to y-direction the x-direction the yz-plane
Mesh size
1 1.34 1 1
[mm]
3.2.2 Creasing and stationary indenting
The maximum Tsai-Wu strength indices for modelling of the creasing, using 2-axial displacement of the creasing roll in the MD, of the corrugated paperboard is shown in Figure 3.7.
Figure 3.7: Maximum Tsai-Wu strength index for creasing where distance from origin is shown on the x-axis. w = 100 mm and l = 80 mm. Creasing roll geometry 0 is used. The depth, δz, is found in Table 7 for a pressure of 4 bar.
Here, the most critical position of the creasing roll can be seen, where the highest maximum Tsai-Wu strength index is found at 10 mm from the origin of the coordinate system. The same investigation for the stationary indenting is shown in Figure 3.8 together with the creasing results from Figure 3.7.
Figure 3.8: Maximum Tsai-Wu strength index for creasing and sta- tionary indenting where distance from origin is shown on the x-axis.
w = 100 mm and l = 80 mm. Creasing roll geometry 0 is used. The depth, δz, is found in Table 7 for a pressure of 4 bar.
The most critical position of the creasing roll for stationary indentation is also found 10 mm from the origin. Therefore, the investigation of the different creasing roll geometries are performed at this position. The maximum Tsai-Wu strength index for stationary indention of the various creasing rolls are shown in Table 9. This at the indentation depth, δz, obtained from the experiments at a pressure of 4 bar (Tabel 7).
Table 9: Maximum Tsai-Wu strength index correlating to the depths, δz, measured in the experiments for each creasing roll ge- ometry at a pressure of 4 bar, see Table 7. w = 100 mm and l = 80 mm.
Creasing roll geometry 0 1 2 3 4 5
Maximum Tsai-Wu
1.2861 1.126 1.0721 1.0534 0.92701 1.1287 strength index [-]
The influence on failure criteria of parameterizating the constant, k, for each ultimate strengths is shown in Figure 3.9.
Figure 3.9: Maximum Tsai-Wu strength index with respect to changes of ultimate strength. w = 100 mm and l = 80 mm. Creas- ing roll geometry 0 used. The depth found in Table 7 at a pressure of 4 bar.
Investigation of the maximum Tsai-Wu strength index for changes in the material parameters are shown in Figure 3.10. Each Young’s modulus and shear modulus were investigated for a 5 % increase and decrease, respectively.
Figure 3.10: Maximum Tsai-Wu strength index for a 5 % change in material properties. The changed material properties are found on the horizontal axis, where the coloring of the bar shows of it is a decrees or increase of the value of the material parameter. w = 100 mm and l = 80 mm. δz = 3 mm and creasing roll geometry 0 was used.
When representing delamination by lowering the shear strength at the middle part of the fluting, the maximum Tsai-Wu strength index changes as shown in Figure 3.11.
Figure 3.11: Maximum Tsai-Wu strength index for different shear strength at middle part of the flutings to delamination. w = 100 mm and l = 80 mm, δz = 3 mm and creasing roll geometry 0 is used.
4. Analysis
The choice of width and length of the corrugated paperboard is highly correlated to the computational costs. One could argue that an as large model as possible will give the most robust model, but this to a higher computational cost than needed. The size of the model of the corrugated board was chosen at the expense of computational cost to ensure that the results are as good as possible. Motivated by the results in Figure 3.2, the width of the model was chosen to 100 mm and the length to 80 mm.
The mesh convergence studies were performed to motivate the choice of the element size. Due to limitations in number of mesh elements, the study were performed part by part. This gives information part by part, liner and fluting etc. The mesh choice for the liner and other parts is therefore chosen separately, all with a converged mesh investigation that ensures saving of the computational cost. As for the size of the paperboard model, the focus was on ensuring a robust model rather than a low computational cost. The final mesh of the corrugated paperboard is shown in Figure 3.6. The measured depths, δz, for creasing, and stationary indenting were very similar, which strengthens the hypothesis that the FE-analysis can be analyzed with stationary indenting. Figure 3.8 shows the difference for creasing and stationary indenting, where the maximum Tsai-Wu strength index coincides at the various locations on the horizontal axis. This further strengthens and in extension concludes that indenting can be used for investigating crack initiation in the top liner of the corrugated paperboard.
5. Discussion
Several factors can affect the variation of mechanical behavior of paperboard and, in extension, the influence of various creasing roll geometries. The variables excluded in this thesis are among others moisture, temperature and the inhomogeneity of the material. These choices were made to limit this thesis and focus on the mechanical behavior. In addition, the material properties used in the FE-analysis do not fully represent the paperboards used for the experiments. However, comparing experi- ments and FE-analysis shows agreement for five out of six creasing roll geometries.
This strengthens the credibility the mechanical analysis and possibility to capture the influence of the creasing roll geometries. The hypothesis of using stationary in- dentation of the creasing roll instead of creasing is verified from the experimental and FEA results. This allowed saving computational costs, which was especially beneficial for the parametric studies. The experimental results show that the creas- ing roll geometries affect the percentage of failure to such an extent that fracture of the top liner could be significantly reduced. The best creasing roll geometry lowered the percentage of failure to 0 % from the original 36 %. Furthermore, the most sensitive material parameters affecting the failure criterion are Young’s moduli, Ex, of the liners in x-direction (Figure 3.9) and the ultimate strength in the cross di- rection of the top liner (Figure 3.10). A variation of these material properties with
±5 % yields a change of the maximum Tsai-Wu strength index with 1.5 % and 5 % (k = 0.95), respectively. The machine used by Packsize AB is pressure controlled.
The pressure-controlled machine can yield varying depths when pushing the creasing rolls into the paperboards. Small variations in material strengths, mechanical behav- ior, or position on the paperboard can give a larger depth than desirable. Another problem that occurs when having a pressure controlled machine is a push through behavior. This means that when a crack initiates on the top liner, the strength of the paperboard is lowered, making the creasing roll to go even further down into the paperboard enhancing the failure probability. Often, the creasing roll needs to encounter a stronger than average region of the paperboard to get the creasing roll back to the wanted indentation depth. To understand the influence of parameters of the roller creasing method fully, more investigations are needed. It is suggested that they should focus on material properties that represent the material used in the experiments better. This would allow a more accurate validation the FE-model.
With a validated model, optimization of the creasing roll geometries, further inves- tigations of the influence of material properties, and various corrugated paperboard geometries can be performed. In addition, the performance of the resulting creasing lines is not included in this thesis work. Other suggested future work is to investigate the bending moment in the creased line, as Cavlin [18] does. He is researching paper- boards, investigating various creasing angles and creasing depths, and studying the resulting bending stiffness when folding at the creasing line. A similar research for corrugated paperboards could give a correlation between creasing depth and creased edge performance, bending moment etc.
6. Conclusions
The experimental results show that the creasing roll geometries significantly affects the number of fractures in the top liner. The best result, yielded by creasing roll 4, lowered the percentage of failure from 36 % to 0 % at a base pressure of 4 bars.
This concludes that the existing creasing roll geometry is not optimized for this type of corrugated paperboard. Furthermore, based on the Tsai-Wu failure criterion, the most sensitive material parameters are Young’s moduli, Ex, of the liners in x- direction and the ultimate strength in the cross direction of the top liner. A variation of these material properties with ±5 % yields a change of the maximum Tsai-Wu strength index with 1.5 % and 5 %, respectively.
References
[1] Holik, H., ”Handbook of paper and board (Chapt 2)”, 1(2), Weinheim: Wiley- VCH, 2013.
[2] Uesaka, T., ”Statistical aspects of failure of paper products” In Mechanics of Paper Products (Chapt 8), Niskanen, K., Ed., Walter De Gruyter, 2012.
[3] Kulachenko, A., Mansour, R., Chen, W. and Olsson, M., ”Stochastic constitutive model of isotropic thin fiber networks based on stochastic volume elements”, Materials, 12(3), p.1-28, 2019
[4] Allansson, A. and Sv¨ard, B., ”Stability and collapse of the corrugated board:
Numerical and experimental analysis”, Master thesis, Lund University, Lund, Sweden, 2001.
[5] Nordstrand, T.M., ”Parametric study of the post-buckling strength of structural core sandwich panels”, Composite structures, 30(4), p.441-451, 1995.
[6] Tsai, S.W. and Wu, E.M., ”A General Theory of Strength for Anisotropic Mate- rials”, Journal of Composite Materials, 5(1), p.58–80, 1971.
[7] Nyman, U. and Gustafsson, P.J., ”Material and structural failure criterion of corrugated board facings”, Composite structures, 50(1), p.79-83, 2000.
[8] Thakkar, B.K., Gooren L.G.J., Peerlings R.H.J. and Geers M.G.D., ”Experimen- tal and numerical investigation of creasing in corrugated paperboard”, Philosoph- ical Magazine, 88(28), 2008.
[9] Gooren, L.G.K., ”Creasing behaviour of corrugated board”, Master thesis, De- partment of Mechanical Engineering, Technische University Eindhoven, The Ned- erlands, 2006.
[10] Holik, H., ”Handbook of paper and board (Chapt 1)”, 1(2), Weinheim: Wiley- VCH, 2013.
[11] Carlsson, L.A. and H¨agglund, R., ”Packaging performance” In Mechanics of Paper Products (Chapt 3), Niskanen, K., Ed., Walter De Gruyter, 2012.
[12] https://www.fefco.org/lca/dscription-of-production-system/corrugated-board- production, European Corrugated Packaging Association, Brussels, Belgium, 20/06/2020.
[13] Foster, G.A., ”Corrugated Boxes” In The Wiley Encyclopedia of Packaging Technology 3rd Edition, Yam, K.L., Ed., John Wiley & Sons, p.164, 2010.
[14] Haj-Ali, R., Choi, J., Wei, B-S., Popil, R. and Schaepe, M., ”Refined nonlienar finite element models for corrugated fiberboards”, Composite Structures, 87(4), p.321-333, 2008.
[15] ANSYS Mechanical APDL Element Reference - release 14, Ansys inc., 2011.
[16] Nyg˚ards, M., ”Behavior of corners in carton board boxes”. In Mechanics of Paper Products (Chapt 4), Niskanen, K., Ed., Walter De Gruyter, 2012.
[17] Li, S., Sitnikova, E., Liang, Y. and Kaddour, A.S., ”The Tsai-Wu failure crite- rion rationalised in the context of UD composites”, Composites Part A: Applied Science and Manufacturing, 102, 2017.
[18] Cavlin, S., Dunder, I. and Edholm, B., ”Creasability testing by inclined rules
— a base for standardized specification of paperboard”, Packaging Technology and Science: An International Journal, 10(4), p191-207, 1997.
33
endix 1 - Creasing roll geometries for exp erimen ts
NAME Isak Hampel Klang DATE 03/04/20TITLE
Cre as ing Ro ll Ge om et ry 0
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
4
O180O200
r0,1
R3
10,3
R 2
° 105
0,80,8 90°
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 1
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
1
R 0,5
O180O200r0,1
0,80,8
L0,52 9 2,8
90° 4
° 120
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 2
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
O176,3B DE TA IL B SC AL E 5 : 1
° 90
° 140
2
R 0,5
R0,5
4
3 2,3
0,80,8 2
r0,1 e0,3
O180O200
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 3
SIZE A4 SCAlE:WEIGHT:e0,3
r0,1
O180O200
A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
O176,32
R 0,5
R0,5
5
° 140
9 3,8
2
90°0,80,8 2
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 4
SIZE A4 SCAlE:WEIGHT:e0,3
A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
O176,3R2
90°0,80,8 2
O180O200
r0,1
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 5
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
1
R0,5 0,58
R 0,51
R1,89
° 150
O180O200
4
2,8 5
r0,1
0,80,8
endix 2 - Creasing roll geometries for FE-mo deling
NAME Isak Hampel Klang DATE 03/04/20TITLE
Cre as ing Ro ll Ge om et ry 0
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
4
O180O200
r0,1 35°
5
0,4
R3
10,3
R 2
° 105
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 1
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
1
R 0,5
° 120
4
O180O200
R0,5 9 2,8
r0,1 35°
5
0,4
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 2
SIZE A4 SCAlE:WEIGHT:A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
° 140
2
R 0,5
R0,5 3 2,3
r0,1 O180O200
5
0,44
35°
NAME Isak Hampel Klang DATE 03/04/20
TITLE
Cre as ing Ro ll Ge om et ry 3
SIZE A4 SCAlE:WEIGHT:r0,1 O180O200
A A SE CT IO N A- A
B DE TA IL B SC AL E 5 : 1
2
R 0,5
R0,5
5
° 140
9 3,8
2 5
0,4435°
